Skip to main content

Information Geometry of Interspike Intervals in Spiking Neurons with Refractories

  • Conference paper
Book cover Advances in Neuro-Information Processing (ICONIP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5506))

Included in the following conference series:

  • 1594 Accesses

Abstract

An information geometrical method is developed for characterizing or classifying neurons in cortical areas, whose spike rates fluctuate in time. When the interspike intervals of a spike sequence of a neuron obey a gamma process with a time-variant spike rate and a fixed shape parameter, the information geometry for semiparametric estimation has given the optimal method from the statistical viewpoint. Recently a more suitable statistical model for interspike intervals is proposed, which have an absolute refractory period. This work extends the information geometrical method and derives the optimal method for the new model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Holt, G.R., Softky, W.R., Koch, C., Douglas, R.J.: Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. Journal of Neurophysiology 75, 1806–1814 (1996)

    Google Scholar 

  2. Shinomoto, S., Sakai, Y., Funahashi, S.: The ornstein-uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex. Neural Computation 11, 935–951 (1999)

    Article  Google Scholar 

  3. Sakai, Y., Funahashi, S., Shinomoto, S.: Temporally correlated inputs to leaky integrate-and-fire models can reproduce spiking statistics of cortical neurons. Neural Networks 12, 1181–1190 (1999)

    Article  Google Scholar 

  4. Shinomoto, S., Shima, K., Tanji, J.: New classification scheme of cortical sites with the neuronal spiking characteristics. Neural Networks 15(10), 1165–1169 (2002)

    Article  Google Scholar 

  5. Shinomoto, S., Shima, K., Tanji, J.: Differences in spiking patterns among cortical neurons. Neural Computation 15(12), 2823–2842 (2003)

    Article  MATH  Google Scholar 

  6. Tiesinga, P.H.E., Fellous, J.M., Sejnowski, T.J.: Attractor reliability reveals deterministic structure in neuronal spike trains. Neural Computation 14, 1629–1650 (2002)

    Article  MATH  Google Scholar 

  7. Amari, S.I.: Differential-Geometrical Methods in Statistics. Lecture Notes in Statistics, vol. 28. Springer, Heidelberg (1985)

    MATH  Google Scholar 

  8. Amari, S.I., Nagaoka, H.: Methods of Information Geometry. Translations of Mathematical Monographs, vol. 191. AMS and Oxford Univ. Press, Oxford (2000)

    MATH  Google Scholar 

  9. Miura, K., Shinomoto, S., Okada, M.: Search for optimal measure to discriminate random and regular spike trains. Technical Report NC2004-52, IEICE (2004)

    Google Scholar 

  10. Ikeda, K.: Information geometry of interspike intervals in spiking neurons. Neural Computation 17(12), 2719–2735 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Miura, K., Okada, M., Amari, S.I.: Estimating spiking irregularities under changing environments. Neural Computation 18(10), 2359–2386 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Shinomoto, S.: Private communication

    Google Scholar 

  13. Shinomoto, S., Tsubo, Y.: Modeling spiking behavior of neurons with time-dependent poisson processes. Physical Review E 64, 41910 (2001)

    Article  Google Scholar 

  14. Godambe, V.P.: Conditional likelihood and unconditional optimum estimating equations. Biometrika 63, 277–284 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  15. Godambe, V.P. (ed.): Estimating Functions. Oxford Univ. Press, Oxford (1991)

    MATH  Google Scholar 

  16. Amari, S.I., Kawanabe, M.: Information geometry of estimating functions in semiparametric statistical models. Bernoulli 2(3) (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Komazawa, D., Ikeda, K., Funaya, H. (2009). Information Geometry of Interspike Intervals in Spiking Neurons with Refractories. In: Köppen, M., Kasabov, N., Coghill, G. (eds) Advances in Neuro-Information Processing. ICONIP 2008. Lecture Notes in Computer Science, vol 5506. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02490-0_89

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02490-0_89

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02489-4

  • Online ISBN: 978-3-642-02490-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics